(a) (15 pts) A net force is applied to a mass m that isinitially at rest on a level frictionless surface. The force varieswith position and is given by F(x)=Ax3/2. The force is appliedtothemassfrompositionsx=0tox=d. Aftertheforcestopsacting,the massthen slides throughalevelfrictionpatchwithcoefï¬cientoffrictionµk.
How far does the mass travel through the friction patch beforecoming to rest? Put your answer in terms of m,g,d, µk,and A.
(b) (5 pts) Now, suppose that instead of the position-varying forceacting on the mass, a time-varyingnetforceF(t)=At3/2 acted on theblock from time st =0tot =t1. After the time-varying force stoppedacting, then the block went through the same friction patch. Forthis new scenario, what would be your approach to solving thisproblem? Briefly explains using equations and/or technical words. Bespeciï¬c to earn full credit. Solving part (b) is not required forfull credit.
